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What: Shares of The Fresh Market (NASDAQ:TFM) jumped on Thursday following a report from Reuters that supermarket giant Kroger (NYSE:KR) wants to acquire the company. At 3:15 p.m. ET Thursday, shares of The Fresh Market were up about 16%, while shares of Kroger were down less than 1%.

So what: According to Reuters, Kroger is in the second round of an auction process for The Fresh Market. Various private equity firms, including Apollo Global Management and KKR & Co., are said to also be interested in potentially acquiring the specialty grocer.

In October, The Fresh Market announced that it would conduct a strategic review of its business and strategy, and this auction process appears to be the result of that plan. The company has faced growing competition from traditional supermarkets like Kroger, which have been increasing the amount of natural and organic foods sold in stores.

The Fresh Market wouldn't be the first upscale chain purchased by Kroger. Back in 2014, the company acquired Harris-Teeter, a North-Carolina based supermarket chain. With The Fresh Market having a market capitalization of about $1 billion, any buyout would likely involve a significant premium to that level.

Now what: There's no guarantee that Kroger will end up winning the auction or that The Fresh Market will sell itself at all. For Kroger, an acquisition would boost its revenue by less than 2%, although The Fresh Market does manage far higher margins than Kroger's existing business.

It's unclear whether a deal will be announced, but investors should remember that buying a stock solely based on the hope that the company will get acquired is rarely a good idea.

Timothy Green has no position in any stocks mentioned. The Motley Fool has no position in any of the stocks mentioned. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.